anfis pd+i based hybrid force/ position control of an industrial

Abstract—A hybrid force plus position controller based on

adaptive neuro fuzzy inference system proportional derivative +

integral (ANFIS-PD+I), with unspecified robot dynamics has

been proposed for a robot manipulator under constrained

environment. The proposed controller has been employed as a

principal controller to tune up orthodox PID gains throughout

the complete trajectory tracking process. The validity of the

proposed controller has been studied using a 6-Degree of

Freedom (DOF) PUMA robot manipulator. Simulation

outcomes illustrates that the projected force / position controller

adheres to the desired path closer and smoother.

Index Terms—Adaptive neuro fuzzy control, degrees of

freedom, force control, position control, robot manipulator.

I. INTRODUCTION

An industrial robot manipulator employs desirable force

normal to a given surface for following a recommended

motion tangential trajectory most of the time. A Modified

Hybrid Control scheme was presented in [1] which

accomplished an accurate position and force control for a

robot manipulator in joint space by specifying the desired

compliance in Cartesian space. A hybrid neuro fuzzy (NF)

position/force control with vibration suppression was

presented in [2], where an adaptive neuro fuzzy inference

system was applied to estimate the inverse dynamics of the

space robot. The quadratic optimization and sliding-mode

based hybrid position and force control approach for a robot

manipulator was presented in [3] where the optimal feedback

control law was derived to decide matrix differential Riccati

equation and a feed forward neural network was applied to

tackle the dynamic model uncertainties. A neural adaptive

control scheme for hybrid force/position control of rigid robot

manipulators was presented in [4]. Based on decomposed

robot dynamics into force, position and redundant joint

subspaces, a neural controller was proposed to tackle the

parametric uncertainties, present in the dynamical model of

the robot manipulator. A novel neuro-adaptive force/position

tracking controller in touch with a surface influenced with

non-parametric uncertainties was proposed in [5] for a robotic

manipulator The configuration dependent dynamical problem

Manuscript received November 9, 2013; revised January 10, 2014.

Himanshu Chaudhary is with the Department of Electrical Engineering,

IITR, India (e-mail: himan.74@ gmail.com, [email protected]).

Vikas Panwar and Rajendra Prasad are with the School of Vocational

Studies & Applied Sciences, GBU, India (e-mail:[email protected]).

N. Sukavanum is with the Department of Mathematics, IITR, India

(e-mail: [email protected]).

of the manipulator in constrained motion was dealt in [6] with

the implementation of a hybrid force/velocity control for

contour tracking tasks of unknown objects performed by

industrial robot manipulators. An adaptive robust hybrid

position/force control technique based on Lyapunov stability

and bound estimation for a robot manipulator was proposed in

[7]. The controller does not need the information of

uncertainty bound. A position/ force controller based on the

principles of invariancy for dividing of the task space into

force and position subspaces was introduced in [8], to

guarantee the overall stability. A hybrid impedance force /

position control scheme was developed and presented in [9]

for a redundant robot manipulator. The outer-loop controller

improves transient performance, while the inner loop consists

of a Cartesian-level potential difference controller, a

redundancy resolution scheme at the acceleration level, and a

joint-space inverse dynamics controller. A stable as well as

generalized architecture for hybrid position/force control is

presented in [10], which can influence both joint positions

and torques. It was shown that kinematic instability is due to

inverse of the manipulator Jacobian matrix. A robust learning

control algorithm for precise path tracking of constrained

robotic manipulators in the presence of state disturbances,

output measurement noises and errors in initial conditions

was presented in [11]. The reference [12] proposed a hybrid

position, posture, force, and moment control for a

six-degree-of-freedom (6-DOF) robot manipulator for the

surface contact work by expansion of the conventional hybrid

position and force control. The issue of hybrid adaptive

network-based fuzzy inference system (ANFIS) tuning

methodology based force/position control of the robot

manipulators mounted on oscillatory was successfully applied

in [13]. When the system is in sliding mode, force, position,

and redundant joint velocity errors will approach zero

irrespective of parametric uncertainties so a novel

sliding-adaptive controller Based on a decomposition of the

rigid robot system with motor dynamics was developed in

[14], which can achieve robustness to parameter variations in

both manipulator and motor. A hybrid adaptive fuzzy control

approach based position/force control of robot manipulators

is proposed in [15] to solve the overwhelming complexity of

the deburring process and imprecise knowledge about robot

manipulators. A fuzzy neural networks based Position/force

controller to deal efficiently with force disturbances signals

was presented in [16], to search the direction of the constraint

surface for an unknown object. There are many theoretical as

well as practical hurdles which are still unachievable because

of unspecified robot manipulator dynamics as well as

environmental complexities. Standard approaches are

ANFIS PD+I Based Hybrid Force/ Position Control of an

Industrial Robot Manipulator

Himanshu Chaudhary, Vikas Panwar, N. Sukavanam, and Rajendra Prasad

International Journal of Materials, Mechanics and Manufacturing, Vol. 2, No. 2, May 2014

107DOI: 10.7763/IJMMM.2014.V2.110

appropriate when one has the precise mathematical modeling

of all the fundamental parameters vital, are available. On the

other hand, most of the time one has to work in real

environment where the dynamic model as well as external

environmental variables are unidentified [17]. Conventional

controllers like PD and PI alone do not perform well in case of

removing steady state error as well as to enhance the transient

response. Recently, some of the hybrid intelligent type fuzzy

proportional integral derivative (FPID) controller techniques

have been combined with conventional techniques and

presented in [18], which illustrates the improved steady state

as well as transient response. A two input fuzzy system (TIFS)

based digital type proportional integral derivative (PID)

controller was presented in [19]. For achieving high

robustness opposed to noise, [20] accumulated twin nonlinear

differentiators with a conventional fuzzy proportional and

derivative (CFPD) controller to develop a different hybrid

fuzzy proportional and derivative (HFPD) controller. To

unravel the nonlinear control snag, [21] integrated the fuzzy

gain scheduling method with a fuzzy proportional, integral

and derivative (FPID) control for industrial robot manipulator.

To eliminates the requirement of precise dynamical models in

Computed Torque Control (CTC) in the presence of

structured/unstructured uncertainty, [22] combined the Fuzzy

Control (FC) concept with CTC to solve the trajectory

control problems of robot manipulators. The reference [23]

presented a Self-Organizing Fuzzy Proportional Derivative

(SOF-PD) control scheme, which exploits the simplicity and

toughness of the plain PD control and enhances its gain, was

offered for robot manipulators. To build and optimize the

fuzzy models [24] proposed a HYFIS( Hybrid neural fuzzy

Inference system), which inculcates the learning capabilities

of neural networks with processing power of fuzzy logic.

while considering the nonlinearities, uncertainties and

external perturbations of an industrial robot manipulator, [25]

proposed some new hybrid ANFIS (Adaptive neuro fuzzy

inference system) control algorithms. The reference [26]

applied ANFIS to address the inverse kinematic problem of

determining a set of joint angles for a specific manipulator

posture, while the robot’s postures and trajectories were

executed in Virtual Reality. An ANFIS based solution was

presented in [27] to replicate the real time performance of an

industrial end effector, So that the controller can facilitate

dissimilar gains with disturbance signals. The reference [28]

used the ANFIS for the designing of a controller based on

inverse kinematic of an industrial robot manipulator.

In the present research paper, a hybrid force/position

control approach is proposed for trajectory control of robot

manipulator, which works well in the absence of anonymous

dynamics of a robot manipulator in a constraint environment.

The constraint has been taken in joint space by restricting the

manipulator to move in Z direction. The proposed

ANFIS-PD+I force/position controller follows the trajectory

exceptionally smoothly with bare minimum error.

Section II establishes the actuator dynamic model for the n

degrees of freedom (DOF) robot manipulator. The hybrid

ANFIS-PD+I force/position controller is discussed in Section

III. Section IV presents simulation outcome to reveal the

efficiency of the proposed controller, followed by conclusions

in Section V.

II. DYNAMICS OF ROBOT MANIPULATOR

The traditional dynamic model of an n DOF robot

manipulator is presumed to be in the subsequent form[29]

( ) ( , ) ( ) ( )mM q q V q q G q F q (1)

where ( ) nxnM q R represents the inertia matrix,

( , ) RnxnmV q q represents the centripetal-coriolis matrix,

( ) RnG q represents the gravity effects, ( ) RnF q denotes

the friction effects, ( ) nt R signifies the torque input

control vector and ( ), ( ), ( ) nq t q t q t R signify link position,

velocity and acceleration correspondingly. If armature

inductance is insignificant in the case of electric motors then

the dynamics of n decoupled armature-controlled DC motors

are

M M M M MJ q Bq F R K v (2)

where nv R is the control input motor voltage,

{ } nM Miq vec q R with Miq is the i

th rotor angle, motor

inertia is MJ , rotor damping constant denoted by MB , MF is

the actuator friction. The actuator coefficient matrices are

constants, specified as

0

0

( / ) 0

0 ( / )

0

0

/ 0

0 /

MiM

Mi

Mi bi Mi ai

Mi bi Mi ai

i

i

Mi aiM

Mi ai

JJ

J

B K K RB

B K K R

rR

r

K RK

K R

(3)

Here aiR is armature resistance, MiK is torque

constant, biK is back emf constant and MiJ is the motor

inertia of the ith

motor. ir is the gear ratio of the coupling

or i i M i

M

q r q

q Rq

(4)

where ir is a constant less then1 if iq is revolute else units of

m/rad if iq is prismatic. By putting Mq from (4) and from

(1), the actuator dynamics for a robot manipulator may be

written as

.. .2 2

2 2

( ) ( )

( )

M M m

M M

J R M q B R V q

RF R F R G RK v

(5)


108

or

.. . .

( ) ( , ) ( ) ( )mM q q V q q G q F q K v (6)

where

.2 2

.2 2

( ) ( ); ( , ) ( )

( ) ; ( ) ( );

M m M m

M M

M q J R M V q q B R V

G q R G F q RF R F K RK

(7)

After including nonlinear unmodelled disturbances, the (6)

can be rewritten as [29]

.. . .

( ) ( , ) ( ) ( )m dM q q V q q G q F q K v (8)

.. .

( ) ( , ) dM q q N q q K v (9)

III. HYBRID ANFIS-PD+I FORCE/POSITION CONTROLLER

DESIGN

A hybrid ANFIS - PD+I force/position controller applied

to six DOF PUMA robot arm has been shown in Fig. 1. The

ANFIS controller applied, is having two inputs and single

output (TISO) structure. The inputs used are position error as

well as integral error ( me ), velocity error ( me ). The integral

error ( me ) has been used simply to perform orthodox integral

action.

Fig. 1. ANFIS-PD+I hybrid force/position controller.

A. Force/Position Controller

The dynamic model of an n DOF robot manipulator with

environmental contact on a prescribed surface is presumed to

be in the subsequent form [29]

( ) ( , ) ( )

( ) ( )

m

T

d

M q q V q q G q

F q J q

(10)

where ( ) , ( )nq t R J q a Jacobian matrix is related with the

touching surface, and is contact forces vector applied

normal to the surface. The restricted surface for robot

manipulator is considered in Z direction in joint space. The

Jacobian matrix is

( )Z

J qq

(11)

The constraint equation reduces the number of degree of

freedom to

1n n m (12)

To find the constraint motion along the Z direction the

reduced order dynamics for robot manipulator is

1 1 1 1 1 1

1 1 1

( ) ( ) ( , )

( ) ( ) ( )

m

Td

M q L q q V q q q

F q G q J q

(13)

where 1

1 1( ) , ( )n

q t R L q is an extended Jacobian matrix

given by

1

1

1

( )

nI

L q Z

q

(14)

The reduced order dynamics describing the motion in the

plane of constraint surface is

1 1 1 dMq V q F G (15)

where

1 1 1 1 1 1( ) ; ( , ) ( ( ) ),

; ; ;

T T Tm

T T T Td d

M L M q L V V q q L L V L M q L

F L F G L G L L

As 1 1( ) ( ) 0J q L q (16)

The suppositions and the necessary properties of the model

given in (6) have been utilized in the proposed controller

development are given as

Property 1: The inertia matrix 1( )M q is positive definite

symmetric and bounded above and below.

Property 2: The matrix 1 1 1 1( ( ) - 2 ( , ))M q V q q is skew

symmetric.

Property 3: 1 1( ) F q a b q for some unknown

positive constants a, b.

Property 4: d c for some unknown positive constants

c.

B. ANFIS Architecture

It combines the learning capabilities of neural networks

with processing power of fuzzy logic. [30] proposed and

explained the use of ANFIS for solving a fuzzy inference

system under consideration having two inputs x and y and one

output z, which contains the rule base of two fuzzy if-then

rules as

Rule 1:

1 1 1 1 1 1 , If x is A and y is B then f p x q y r

Rule 2:

2 2 2 2 2 2 , If x is A and y is B then f p x q y r

During the training of the network, the input is propagated

layer by layer in forward direction while the error is

propagated in backward direction. In layer 1, the member ship

function is applied on premise parameters. To show the firing

strength, layer 2 multiplies the incoming signals. Layer 3

calculates the firing strength of the signals received and


109

forwards it to layer 4, which calculates an adaptive output for

giving them as input to the layer 5, which computes the

overall output. The procedural equations used at different

layers are given in the flowchart as shown in Fig. 2.

Then the output of the hybrid ANFIS-PD+I force/position

controller is, therefore

5i

0

( ) [ ( ) ]*

t

i m uu t L K e t dt K (17)

Here 5iL is the output ANFIS-PD controller. Thus a hybrid

force position controller has the structure

( ) ( )Td fu t J q K (18)

Fig. 2. Flow chart for using ANFIS procedure.

IV. SIMULATIONS AND RESULTS

For showing the efficiency of the suggested hybrid

ANFIS-PD+I force/position controller, the simulation has

been performed for a six DOF PUMA robot manipulator

using MATLAB 2012b by considering the PUMA-560 robot

manipulator dynamics from [31]. The following four cases

have been considered to study the simulation results:

1. Complete(C): In this, we developed all the controllers

based on (8), which represents the complete dynamical

system including actuator dynamics.

2. Without Friction (WF): In this, we developed all the

controllers based on (8), which represents the complete

dynamical system including actuator dynamics. The only

difference with the first case is that friction term is absent.

3. Without Gravity (WG): For this case we have designed

the controllers based on a modified version of (8), which lacks

of gravity term in it only.

4. Without External Disturbances (WED): controllers

are developed on a modified dynamic model based on (8) for

this case. The only difference from first case is the absence of

external disturbances.

The working efficiency of the controller has been analyzed

by the data recorded through simulation for all the cases,

which is shown in the following figures. The error tracking

response of hybrid ANFIS-PD + I force/position controller is

shown in the Fig. 4, which clearly depicts that the proposed

controller is efficient enough to track the desired trajectory

with minimum steady state error.

0 5000 10000 15000-4

-2

0

2

4

6

Error

Points for 15 sec duration

Joint1

Joint3

Joint4

Joint5

Joint6

Fig. 3. Tracking error of hybrid FPD+I force/position controller.

The performance of the controller can be checked through

their output response which is shown in the Fig. 5.

0 5 10 15-6

-4

-2

0

2

4

6

8

Time(sec)

Desired T

raje

ctory V

s. A

ctual T

raje

ctory

Desired Joint1

Desired Joint3

Desired Joint4

Desired Joint5

Desired Joint6

Actual Joint1

Actual Joint3

Actual Joint4

Actual Joint5

Actual Joint6

Fig. 4. Output response of hybrid ANFIS-PD+I force/position controller.

The proposed controller is able to deal with the continuous

as well as discontinuous friction, gravity and other external

disturbances while successfully following the desired

trajectory by looking at the Fig. 5. One can see that the

proposed controller is successfully following the desired

trajectory with minimum errors. The simulation experiments

were conducted for 24 observations with the identical gain

value statistically, to study the performance of the proposed

controller with other controllers. Dissimilar trajectories,

dissimilar robot parameters and dissimilar simulation time (5s,

10s, and 15s) have been employed for all 24 observations.

The RMS values of path errors for joint angles q1 to q6 are

calculated for each experiment. The RMS values average for

all four cases has been calculated over 24 sets are given in

Table II and Table III.

The two desired trajectories are taken for which the whole

data has been recorded. The trajectories are: (I) sin(2t) (II)

0.15cos((pi/2)t). The friction term as well as the gravity term

and external disturbances taken are as follows:


110

TABLE I: RMS ERROR FOR TRAJECTORY SIN (2T)

Joint

Angle

5 seconds 10 seconds 15 seconds

C WF WG WED C WF WG WED C WF WG WED

q1 0.03 0.02 0.03 0.03 0.03 0.02 0.03 0.03 0.03 0.02 0.03 0.03

q3 0.11 0.10 0.10 0.10 0.11 0.10 0.10 0.10 0.11 0.10 0.10 0.10

q4 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03

q5 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

q6 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09

TABLE II: RMS ERROR FOR TRAJECTORY 0.15COS ((PI/2)T)

Joint

Angle

5 seconds 10 seconds 15 seconds

C WF WG WED C WF WG WED C WF WG WED

q1 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02

q3 0.07 0.06 0.07 0.07 0.07 0.06 0.07 0.07 0.07 0.06 0.07 0.07

q4 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

q5 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08

q6 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10

2 2 3 2

2 3 4 5 2 3

2 3 4 5

2 3 5 2 3 4 5

0

37.196*cos( ) 8.445*sin( ) 1.023*sin( )

0.248*cos( )*cos( )*sin( ) sin( )

0.028*sin( )*sin( )*sin( )

0.028*[cos( )*sin( )] [sin( )*cos( )]

0

t t t t

t t t t t tG

t t t t

t t t t t t t

2 2 2

3 3 3

*sin 3 ' 0.2*sin * '

*0.5*sin(2 ) '*1.2* 0.1*sin( )* '

*1.2*sin( ) '*0.8* 0.1*sin( )* ',

0 0

0 0

0 0

dc dd

q t q t q

q t q t t q

q t q t t q

10 2* ( * )

5 2* ( * )

2 2* ( * ),

0 2* ( * )

0 2* ( * )

0 2* ( * )

c d

randomwaveform pi t

randomwaveform pi t

randomwaveform pi tF F

randomwaveform pi t

randomwaveform pi t

randomwaveform pi t

where ; .d dc dd c dF F F

The actuator parameters are:

1

[0.189 0.219 0.202 0.075 0.066 0.066]

1000

[2.1 2.1 2.1 6.7 6.7 6.7]i

bi Mi

a

a

K K

L

R

Gear Ratio = [62.61 107.36 53.69 76.01 71.91 76.73]

All other parameters are taken from [31]. The PID gain

parameters are taken as:

[20 10 10 10 8 6]

[20 8 3 2.0 2.2 2.0]

[0 2.5 1 0 0 0]

P

D

I

K

K

K

The mean RMS error of the proposed ANFIS-PD+I force

position controller is lower.

V. CONCLUSION

A hybrid ANFIS-PD+I force/position controller is

suggested for the trajectory control of a robot manipulator

arm with unspecified robot dynamics in real constraint

environment. The system performance has been investigated

extensively through simulation outcomes. The 6 DOF PUMA

robot manipulator’s simulation results are used to show that

the proposed controller is efficient enough to handle odd

situations while following the desired trajectory. The

practicability of the projected controller with an appropriately

defined automatic tuning of the ANFIS system using

evolutionary techniques may be explored further.

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and inertial parameters of the PUMA 560 arm," in Proc. IEEE Int.

Conf. on Robotics and Automation, 1986, pp. 510-518.

Himanshu Chaudhary received his B.E. in

electronics and telecommunication from Amravati

University, Amravati, India in 1996, M.E. in

automatic controls and robotics from M.S. University,

Baroda, Gujarat, India in 2000. Presently he is a

research scholar in Electrical Engineering Department,

IIT Roorkee, India. His area of interest includes

industrial robotics, computer networks and embedded

systems.

Viaks Panwar received B.Sc. (mathematics) degree

from Meerut University, India in 1998. He received

M.Sc. and Ph.D. degree in mathematics from the IIT

Roorkee, India in 2000 and 2008 respectively. He also

served as an assistant professor (July 31 2004 – 9

March 2010) at Chaudhary Devi Lal University Sirsa,

Haryana. He also worked as an assistant professor

(March 10 2010 – 16 August 2010) at Defence

Institute of Advanced Technology, (Deemed

University) Pune, Maharashtra. Presently he is working as an assistant

professor from 18 August 2010 at Gautam Buddha University, Greater

Noida, Uttar Pradesh.

N. Sukavanum was born in India in 1957. He received

B.Sc. (Maths) degree from University of Madras, India

in 1977 and M.Sc. (Maths) from the same university in

1979 and Ph.D. (Maths) from IISC Banglore, India in

1985 respectively. He has served as a scientist-B in

Naval Science and Technological Laboratory, DRDO,

Vizag, and as a research scientist in I I T, Bombay. He

also worked as a lecturer at Birla Institute of

Technology and Science, Pilani, Rajasthan from 1990

to 1996. He worked as an assistant professor in Mathematics Department at

Indian Institute of Technology, Roorkee during May 1996–April 2004.

Presently, he is a professor in the Department of Mathematics, Indian

Institute of Technology Roorkee, Roorkee (India). He has published 60

papers in various journals/conferences. He has guided nine Ph.D’s, and

presently six Ph. D’s are under progress. His research interests include

nonlinear analysis, control theory and robotics and control.

Rajendra Prasad received B.Sc. (Hons.) degree from

Meerut University, India in 1973. He received B.E.,

M.E. and Ph.D. degree in electrical engineering from

the University of Roorkee, India in 1977, 1979 and

1990 respectively.. He also served as an assistant

engineer in Madhya Pradesh Electricity Board

(MPEB) from 1979- 1983. Currently, he is a professor

in the Department of Electrical Engineering, Indian

Institute of Technology Roorkee, Roorkee (India). He

has more than 32 years of experience of teaching as well as industry. He has

published 176 papers in various journals/conferences and received eight

awards on his publications in various national/international

journals/conferences proceeding papers. He has guided Seven PhD’s, and

presently six PhD’s are under progress. His research interests include

control, optimization, system engineering and model order reduction of large

scale systems and industrial robotics.


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anfis pd+i based hybrid force/ position control of an industrial

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